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Examples of Decrypting with RSA

We have already looked at how to encrypt plaintext P given the public information [n, e] into ciphertext C. We are now going to look at some examples of decrypting C back into plaintext given the decryption key d. We note the following congruence holds:

(1)

\begin{align} P \equiv C^d \pmod {n} \end{align}

Example 1

We know that $P \equiv C^d \pmod {n}$, or more appropriately, $P \equiv 106^{11} \pmod {143}$. We note that we don't even need the encryption key e in these scenarios. We will now evaluate this congruence as follows: